It's hard to look at code and say if it looks okay. The best way to check is to run it and see if you get any errors, and if not, to check the results to see if you get what you expect.

Estimates are not standardized. Both Std and StdYX are standardized. Std uses the variances of latent variables. Because you have none, they are therefore the same as the raw coefficients. Same for indirect effects. See the user's guide for more information.

I didn't get any errors, but things are not always as they seem. I think I have done enough now, though, to be confident in that part of the code.

And thank you for clarifying about the raw and standardized estimates.

What I am trying to do now is a direct comparison of the two mediators in the model, to determine whether one is a stronger predictor. So, I would like to create a contrast of the two specific indirect effects (specific indirect effect for mediator 1 minus specific indirect effect for mediator 2) and to bootstrap a CI for it. Can you provide some guidance on how to code this in the program above?

You can use MODEL CONSTRAINT to create indirect effects and test their equality. Example 3.10 shows an example of how MODEL CONSTRAINT is used. See also the full description of MODEL CONSTRAINT in the user's guide. You can then use the CINTERVAL option to obtain bootstrapped confidence intervals. See the description of the CINTERVAL option in the user's guide.

The z-score should be compared to a symmetric confidence interval. The fact that the bootstrapped confidence interval does not behave like the symmetric confidence interval suggests you should use the bootstrapped confidence interval.

I am a relatively inexperienced Mplus user and was wondering if FIML is used (by default) for path analysis?

Specifically, does FIML handle missing data for (manifest) predictor and mediator variables (where some are categorical), as well as control variables that are included in the model via correlations with the predictor variables and pathways to the mediators.

FIML is used for all endogenous variables. It is not applied to exogenous variables. The theory does not cover this. If you want it to be applied to exogenous variables, you must bring all observed exogenous variables into the model by mentioning their variances in the MODEL command. When you do this, they are treated as endogenous variables and distributional assumptions are made about them.

One additional question: can categorical predictor and mediator variables (with more than 2 categories) be included in the model of a path analysis (by creating dummy variables) even if they cannot be MVN?